Simulating Virtual Players for UNO without Computers

TL;DR

The paper tackles the problem of simulating virtual players in physical UNO without computers while preserving the secrecy of each player's hand. It introduces a card-based protocol that can uniformly select a valid move from a virtual player's hand or report that no valid move exists, using a suite of primitives such as pile-scramble shuffles, Boolean-bit encoding, a Six-Card AND protocol, and a Modified Covert Lottery protocol. The approach is proved correct and information-theoretically secure, and is shown to generalize to other turn-based games like Sevens, Hearts, and Dominoes. This work enables verifiable, privacy-preserving virtual-player behavior in real-world settings and offers a framework for extending card-based simulations to a broader class of games.

Abstract

UNO is a popular multiplayer card game. In each turn, a player has to play a card in their hand having the same number or color as the most recently played card. When having few people, adding virtual players to play the game can easily be done in UNO video games. However, this is a challenging task for physical UNO without computers. In this paper, we propose a protocol that can simulate virtual players using only physical cards. In particular, our protocol can uniformly select a valid card to play from each virtual player's hand at random, or report that none exists, without revealing the rest of its hand. The protocol can also be applied to simulate virtual players in other turn-based card or tile games where each player has to select a valid card or tile to play in each turn.

Figures (1)

• Figure 1: From left to right: $7^R$ , $S^Y$ , $R^G$ , $+^B$ , $W$ , and $D$